Rodriguez connected off Junichi Tazawa of the Boston Red Sox in the eighth inning Friday night to reach the milestone with his sixth home run in a successful return from a yearlong drug suspension.
"Congratulations to Alex Rodriguez on his 660th home run," Mays said in a statement. "Milestones in baseball are meant to be broken and I wish him continued success throughout his career."
When told of that statement, Rodriguez appeared emotional and said, "I love Willie. He's one of my heroes. I'm speechless."
Homer 660 was hit nearly five years after Rodriguez became the youngest player to reach 600 — on Aug. 4, 2010.
Because of injuries and serving the longest performance-enhancing drug ban in major league history, A-Rod went 1,731 days between historic homers, 306 more than Mays, The Say Hey Kid. Home run king Barry Bonds didn't even need two years (612 days) to reach his Godfather's mark after hitting his 600th, according to STATS.
Nearing 40 with two years after this season left on his contract with New York, Rodriguez trails only Babe Ruth (714), Hank Aaron (755) and Bonds (762) in baseball's elite club.
Rodriguez pinch-hit for DH Garrett Jones with the score tied 2-2 with one out in the eighth and hit a 3-0 fastball over the middle of the plate from Tazawa into the left field seats above the Green Monster. He was booed when he came to bat and as he rounded the bases.
Asked how Rodriguez is able to tune out those boos, manager Joe Girardi said, "He's had a lot of practice at it."
As he crossed home plate, Rodriguez slapped hands with Stephen Drew, the next batter, while his teammates clapped in the dugout but did not go out to greet him. He then jogged there where they gave him high fives and slapped his back.
Asked after the game how fans should remember No. 660, Rodriguez said: "I don't know. I know that I'm very excited. A year ago today I never thought I'd be hitting home runs and helping the Yankees win. Being in the middle of it is fun again."
As the slugger quickly closed in on the mark with a surprisingly strong start that's made him the most dynamic player on the AL East leaders, the team virtually ignored his pursuit of Mays — even leaving homer No. 660 off the daily sheet listing players' approaching milestones.
When Rodriguez and the Yankees negotiated a new 10-year, $275 million contract in December 2007, the sides signed a separate $30 million marketing agreement that called for $6 million each for up to five accomplishments, payable within 15 days of designation by the team. The accomplishments were contemplated to be home runs 660, 714, 755, 762 and 763.
The Yankees, though, are thinking about letting the milestones pass without making a designation. With his suspension for his involvement in the Biogenesis performance-enhancing drug scandal, the marketing possibilities for the milestones have been ruined, the Yankees appear to be set to argue.
"Those things will take care of themselves," Rodriguez said after the game.
A failure to declare a milestone and make a payment likely would trigger a grievance on Rodriguez's behalf by the Major League Baseball Players Association. Barring a settlement, the case would be heard by an arbitrator.
Once seen as the player who would restore credibility to baseball's cherished home run title in the Steroids Era, Rodriguez's storied career from No. 1 draft pick to three-time MVP was first tarnished in 2009 when he admitted using steroids from 2001-03 with Texas.
It doesn't help that during his failed fight to overturn a suspension for his involvement in Biogenesis, Rodriguez angered the Yankees by suing, among others, the team physician for the treatment of a hip injury that resulted in surgery. The lawsuit was eventually dropped.
Before the game, Joe Girardi said he wanted Rodriguez to hit No. 660 as soon as possible but also wanted to rest him with a day game coming up Saturday.
"But my job is not to be caught up in milestones," he said, "but to be caught up with what is the best lineup you field that day.
"But I do want to get it out of the way because I think ... as much as a player you try not to think about it, it's impossible. And the sooner we get it out of the way the better."
Rodriguez hit homer No. 100 in August 1998 with Seattle, No. 200 in May 2001 and No. 300 in April 2003 with Texas. His 400th in June 2005 and 500th on Aug. 4, 2007. No. 600 came three years later, to the day.
After homering twice at Tampa Bay on April 17, Rodriguez was batting .344 with four homers. Since then was 5 for 37 with one homer and two RBIs in 10 games going into Friday's game.
He hit No. 659 on Sunday but had one of his worst games Wednesday when he matched his major league career-high with four strikeouts, went 0 for 6 to set a personal mark for most hitless at-bats and grounded into a game-ending double play in the Yankees' 3-2, 13-inning loss to the Tampa Bay Rays.
AP Sports Writer Howie Rumberg in New York contributed to this report.